Related papers: Stochastic Desertification
A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
Phase transitions are divided into first-order phase transitions and continuous ones in current classification. While the latter shows striking phenomena of scaling and universality, the former is generically characterized by discontinuous…
The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that…
We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but…
We study sandpile models as closed systems, with conserved energy density $\zeta$ playing the role of an external parameter. The critical energy density, $\zeta_c$, marks a nonequilibrium phase transition between active and absorbing…
We consider the extinction regime in the spatial stochastic logistic model in $\mathbb{R}^d$ (a.k.a. Bolker--Pacala--Dieckmann--Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space…
Recently, Lipowski [cond-mat/0002378] investigated a stochastic lattice model which exhibits a discontinuous transition from an active phase into infinitely many absorbing states. Since the transition is accompanied by an apparent power-law…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
Starting from an ideal crystalline state, we numerically study a nonequilibrium dynamical order- disorder transition promoted by the application of a periodic shearing protocol at low temperatures in model systems in two and three…
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…
The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from…
Strong eastward jets at the equator have been observed in many planetary atmospheres and simulated in numerical models of varying complexity. However, the nature of the transition from a conventional state of the general circulation, with…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
The idea of a metapopulation has become canonical in ecology. Its original mean field form provides the important intuition that migration and extinction interact to determine the dynamics of a population composed of subpopulations. From…
We observe a novel 'multiple-descent' phenomenon during the training process of LSTM, in which the test loss goes through long cycles of up and down trend multiple times after the model is overtrained. By carrying out asymptotic stability…
We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations.…
We consider disorder-order phase transitions in the three-dimensional version of the scalar noise model (SNM) of flocking. Our results are analogous to those found for the two-dimensional case. For small velocity (v <= 0.1) a continuous,…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
A demographic Allee effect occurs when individual fitness, at low densities, increases with population density. Coupled with environmental fluctuations in demographic rates, Allee effects can have subtle effects on population persistence…